Amorphous and nanocrystalline materials, including nanostructured bulk and nanoporous materials, have different properties than crystalline bulk materials. This is true for inorganic compounds, organic or organometallic materials, and metal-organic complexes. Examples include metallic nanoparticles and nanomaterials; organic pigments, where color may depend on crystallite size; organic semiconductors, where optical and electrical properties depend on crystallinity; and pharmaceutical compounds, where nanocrystalline and amorphous materials generally show increased solubility and bioavailability (Kim et al., 2008, Yu, 2001). Several active pharmaceutical ingredients (APIs) are industrially produced as nanocrystalline or amorphous powders (Prasad et al., 2010) through technologies such as cryomilling, melt extrusion, spray drying or rapid precipitation in the presence of crystallization inhibitors. Moreover, some APIs are produced and distributed in amorphous forms because they cannot be crystallized at all.
The properties of these amorphous or nanocrystalline materials depend strongly on their synthesis or processing conditions. A single “amorphous state” typically does not exist, but there can be substantial structural differences at the nanoscale for materials having an identical chemical composition but different processing history. Indeed, DSC, IR and Raman data reflect variations in analytical data of different “amorphous” batches of the same molecular system.
Despite the need for methods to characterize these materials, however, when the size, or range of structural coherence, of nanomaterials becomes small (e.g., less than 10 nm), traditional powder diffraction techniques, such as, e.g., the Rietveld method (Rietveld, 1969; Young, 1993), typically fail to yield reliable structural information (Billinge & Levin, 2007; Palosz et al., 2002). The atomic pair distribution function (PDF) analysis of x-ray and neutron powder diffraction data has shown itself to be a powerful method for nanostructures determination in this regime. Recently, the development of fast data collection strategies using 2D detectors, coupled with modeling improvements have allowed this approach to become broadly applied in many different chemical studies. During the last two decades, x-ray diffraction (XRD) and neutron diffraction (ND) have been the primary probes to obtain PDF data from structurally challenging materials.
PDF analysis has been a standard tool for the investigation of inorganic liquids and glasses for decades (Warren 1969, Klug & Alexander, 1974, Wagner 1978, Waseda, 1980, Wright 1985, Barnes et al., 2003). In recent years the PDF methodology was extensively applied to study nanostructured materials using short wavelength (epithermal) neutrons and high energy X-rays (Egami & Billinge, 2003; Billinge & Kanatzidis, 2004; Billinge 2008; Young & Goodwin, 2011). It was successfully applied to molecular compounds, including C60 (Egami, and Billinge 2003), pharmaceutical materials (Billinge et al, 2010, Dykne et al. 2011), organic pigments (Schmidt, 2010), organometallic compounds (Petkov & Billinge, 2002) and metal-organic complexes (Wolf et al., 2012).
The powder diagrams for PDF analysis are usually recorded with neutron spallation sources or X-ray synchrotron sources. Generally, laboratory X-ray data can only yield sufficient quality PDFs for fingerprinting when a short-wavelength source (Mo or Ag anode) is used (e.g., see Dykne et al., 2011). Although this experimental setup can be realized in a laboratory, these instruments are very rare. Thus, the instrumental factors present a barrier to a broader application of the PDF method as a general characterization tool. A PDF experiment using electrons does not have this limitation: transmission electron microscopes (TEMs) are available at many labs. Furthermore, TEMs provide great flexibility when it comes to the measurement parameters. An operator can easily change the camera length thus setting various Q-ranges and electron wavelength if necessary. Furthermore, the operator can easily switch between imaging and diffraction mode, and can thus select from which area of the sample the diffraction pattern should be recorded. All these possibilities make PDF analysis from electron diffraction data an attractive alternative to X-rays or neutrons.
Electron diffraction (ED) has been long used for structure characterization of single nanocrystals (Dorset 1995). Due to the significant contribution of multiple scattering, ED was rarely used as an ab initio structure analysis technique, mainly supporting structure analysis based on a combination of other structural methods: X-ray powder diffraction (Gorelik et al., 2010), NMR (Lotsch et al., 2007), computational techniques (Voigt-Martin, 1995). Recently, with the development of 3D electron diffraction techniques, ab initio structure analysis of organic materials became possible (Kolb et al., 2010; Gorelik et al., 2012).
Powder electron diffraction (resulting in ring patterns) is usually used for structural fingerprinting (Làbàr, 2004; Moeck & Rouvimov, 2009). The intensity variations within the rings may also be used for texture analysis of nanocrystals (Gemmi et al., 2011), but usually the rings are azimuthally integrated into 1D diffraction profiles. Obtaining quantitatively reliable powder diffraction intensities from electron microscopes is very rare, with only a few examples of a quantitative structural analysis of powder electron diffraction data in the literature, all from inorganic compounds (Weirich et al., 2000, Kim et al., 2009, Luo et al., 2011). There are a number of reasons, including the strong tendency for electrons to diffract dynamically, the difficulty of obtaining good powder averages from such small volumes of material, and the propensity for the electron beam to damage the sample. Rietveld refinement of organic compounds from powder electron diffraction data has never been done so far.
A limitation of using electrons for quantitative structural studies can be that they interact with the material. Multiple scattering can be important in the resulting scattering which, in general, requires the use of dynamical scattering theory to be interpreted (Cowley, 2004) quantitatively and the simple kinematical scattering theory used in x-ray crystallography (Warren, 1990) and PDF analysis (Warren, 1990; Debye, 1915) may not be strictly valid. This can be circumvented when sample volumes are sufficiently small that multiple scattering events are not of high probability before the electrons exit the sample (e.g., typically a few nm of thickness), or when the scattering from the samples is highly incoherent, for example, the scattering from amorphous materials and away from zone axes in a crystal. In these latter cases there can be still significant multiple scattering, but it is typically sufficiently incoherent that it can be treated as a background and subtracted and the resulting coherent signal can be treated kinematically. This has been used in the rapidly growing field of electron crystallography, and has been demonstrated in previous work of electron diffraction from glasses (see, e.g., Moss et al., 1969; Hirotsu et al., 2003; Norenberg et al., 1999), although no quantitative modeling of the ePDF was attempted in those studies. In this respect, the study of small nanoparticles can be particularly favorable. The samples are typically thin, limited to the diameter of the nanoparticles which may be dispersed on a grid in a dilute way, and the structure is typically less coherent than from crystals because of the finite size effects that significantly broaden Bragg peaks and the often lower symmetries of nanoparticle structures due to surface and bulk relaxations. Fortuitously, the approximations are typically satisfied precisely for the small nanoparticles that can be most beneficially studied using PDF methods.
It is also possible that the interaction of the electron beam with a sample that is organic, organometallic, or a metal-organic complex, can damage the sample and alter the very structure that it is trying to measure. The methods described herein allow the intensity of the beam to be calibrated so that the resulting PDF remains reliable.
Exemplary embodiments of the present disclosure can provide methods, apparatuses, and computer-readable medium for obtaining quantitatively reliable PDFs from a normal transmission electron microscope (TEM) found in many research labs. For example, the resulting electron PDFs (ePDFs) can be modeled to extract quantitative structural information about the local structure using PDF refinements programs such as, e.g., PDFgui (Farrow et al., 2007). This can open the door to broader application of PDF methods for nanostructure characterization since TEM is typically already a routine part of the nanoparticle characterization process (Wang et al., 2000; Won et al., 2006), whereas x-ray PDF (xPDF) and neutron PDF (nPDF) studies typically require (or benefit from) access to intense synchrotron based x-ray and neutron sources. Accordingly, exemplary embodiments of the present disclosure can facilitate obtaining quantitative structural information, similar to that normally obtained from a Rietveld refinement in bulk materials, from nanoparticles with little additional effort. Embodiments of the present disclosure also can complement high resolution TEM by getting an average signal from a large number of nanoparticles rather than giving information from a small part of the sample that may not be representative.
The ability to obtain the real-space images and the diffraction data suitable for structural analysis at the same time and from the same region of material can be a large advantage, resulting in more complete information for the characterization of the sample. In some cases the small quantity of material required for ePDF, compared to xPDF and nPDF measurements, can also be a major advantage, as well as the ability to study thin films. In situations where the most information possible is required about a material, it can be desirable to carry out ePDF studies in conjunction with xPDF and nPDF studies, making use of the complementarity of these probes.
Exemplary embodiments of the present disclosure can be used/implemented/utilized to provide a collection of electron diffraction (ED) data resulting in quantitatively refinable ePDFs from several nanoparticle systems, which can be successfully modeled using standard PDF modeling software, demonstrating that exemplary embodiments of the present disclosure can be a viable and potentially powerful technique for nanoparticle studies.
Additional methods of analysis can also be found in U.S. patent application Ser Nos. 12/802,064, 13/310,683, 61/500,787, 61/525,602, 61/563,258, and 61/510,280, the entire contents of which are hereby incorporated by reference.